# Implementing a Non-Uniformly Spaced Tapped Delay Line Channel Model

Question:
Since you are good on fundamentals I would like to ask you a question that puzzles me. LTE channels models are defined at irregular time intervals as shown in [1].

The EPA, EVA and ETU channel taps can best be described as being sampled at multiples of 10 nsec. However, LTE signal is sampled at multiples of 3.84 MHz (Ts=260.416667 nsec). So how does one perform convolution operation.

Empirical multipath channel is usually characterized as a τ-spaced tapped delay line (TDL), whose power delay profile (PDP) is either uniformly spaced, or more frequently, spaced with arbitrary time delay(s). Converting a τ-spaced empirical model to a more tractable T-spaced (sampling time-spaced) statistical model will greatly facilitate the link-level simulation and performance evaluation of the broadband digital wireless system. The practical approaches to accomplish this task could be either approximation or interpolation,

1. Approximation
a. Ceil or Floor a τ-spaced tap to the neighbouring sampling time.
b. Split the energy of a τ-spaced tap to the adjacent sampling times.
2. Interpolation
An Ideal Bandlimited (sinc) Interpolator can fulfil the goal.

It should be noted that although T-spaced statistical model is simpler for analysis, τ-spaced empirical model represents the channel more accurately.

[1] http://www.steepestascent.com/content/mediaassets/html/LTE/Help/PropagationConditions.html

#### Author: John (YA)

John has over 15 years of Research and Development experience in the field of Wireless Communications. He has worked for a number of companies around the world including Qualcomm Inc. USA. He has an MS in Electrical Engineering from Virginia Tech USA and has published his work in international journals and conferences.

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1. Skymn says:

hi!!!